In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).
There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.
A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true.
Fallacy is a false statement wrapped around the statement of reasoning, in order to convince the listener of an argument. A fallacy is an argument itself. In a conversation, an argument is made to cause the listener to be convinced of the conclusion the speaker is making, however the argument is incorrect or false. In Wikipedia, a fallacy is described as follows: http://en.wikipedia.org/wiki/Fallacy “In logic and rhetoric, a fallacy is a misconception resulting from incorrect reasoning in argumentation. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (e.g. appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure the logical argument, making fallacies more difficult to diagnose. Also, the components of the fallacy may be spread out over separate arguments.”
It is important that we know about all kinds of fallacies in order not to fall in a conversational trap. To get a detail description of fallacies, definition of an argument, and different kinds of fallacies, check the following link: http://www.nizkor.org/features/fallacies/. This link describes different components of fallacies, categorizes fallacies in detail and gives examples for each. Each category of fallacy is summarized below, copied from the mentioned article, along with a brief example of each. For detail descriptions and examples, one can check the mentioned site.
Fallacy I: Ad Hominem
A says to B; you are telling me that you do not believe in abortion. Being a Christian priest, you support what Pope says and you follow anything he believes in, including prolife issues (being a priest does not necessarily make one against abortion).
Fallacy II: Ad Hominem Tu Quoque
A says to B that killing animals for their skin and flesh is morally wrong. B says to A that his statement is incorrect because he is wearing a fur coat and eating a beef sandwich (if A’s action does not match his words he becomes a hypocrite, however his statement or his action may not be wrong).
Fallacy III: Appeal to Authority
A says to B that abortion is wrong because the most famous and important person on earth, professor Dooblidoo who is a nuclear physicist, believes that abortion is wrong (having authority in a subject does not make one expert in all subjects).
Fallacy IV: Appeal to Belief (Appeal to Popularity)
A says to B that religious beliefs are the best philosophy of life. B asks why. A says because most of the people believe in religions (most of the people believing in something does not make it right).
Fallacy V: Appeal to Common Practice
A says he is going to church, and asks B what she is doing. B says that she did not think he was religious. A says that since everyone he knows goes to church, so does he (anything that is a common practice in a society does not necessarily mean that the practice should be followed by everyone in that community).
Fallacy VI: Appeal to Consequences of a Belief (Wishful Thinking)
A claims that believing in big bang makes people not to look forward to a life after their death. Since it has a negative consequence, therefore we should not believe in big bang (prediction of the consequence of doing or not doing something, right or wrong, does not necessitate support of that action or that inaction).
Fallacy VII: Appeal to Emotion
Going door to door, someone is asking people for money to help children, presenting them with pictures of innocent children in poor physical conditions (making a judgment on a subject requires one’s logical scrutiny).
Fallacy VIII: Appeal to Fear (Scare Tactics, Appeal to Force, Ad Baculum)
One is asking people in a religious temple to believe in God or they will be burned in the hell fire (beware of those using fear in order to get their aims).
Fallacy IX: Appeal to Flattery
A tells B how much he thinks she is beautiful and smart and how much she inspires his artistic mood. Then, he asks B to go out with him (when someone is flattered so much, it makes it hard to refuse a favor).
Fallacy X: Appeal to Novelty
A informs B of his plan to buy a second hand car he has in mind. B tells him to buy a new car since a new car is safer with more amenities and a better look (it does not necessarily mean that a new car in all respects is better than an old car).
Fallacy XI: Appeal to Pity
A tells B that abortion is killing little innocent babies (one should be careful of arguments that create a sense of feeling sorry for the person).
Fallacy XII: Appeal to Popularity
A informs B that he will convert to Islam since it is the most growing religion. B asks why such a religion. A confesses that considering the popularity and number of people believing in this religion, something should be good about it (popularity does not make something true and right).
Fallacy XIII: Appeal to Ridicule
A tells B laughingly “you are telling me that an embryo is not a human and killing it is not killing a person? How can you not have enough knowledge to know what a human being is?” (One ridiculing an idea does not necessarily make the idea incorrect).
Fallacy XIV: Appeal to Spite
A reminds B of the last bloody demonstration and prevents her from attending it (an event does not necessarily unfold again).
Fallacy XV: Appeal to Tradition
A reminds B that people have believed in God for thousands of years, so there should be a God (a tradition has its own advantages and disadvantages).
Fallacy XVI: Bandwagon
A threatens B that he will talk to all friends to reject her from the group if she does not change her attitude towards abortion (fear of being rejected or peer pressure is a fallacy).
Fallacy XVII: Begging the Question
A tells B that God exist. B asks what proof he has, A responds that because Bible says that. B asks why she should believe in Bible. A says because Bible was written by God (a point cannot be proven in a circular argument).
Fallacy XVIII: Biased Sample (Biased Statistics, Loaded Sample, Prejudiced Statistics, Prejudiced Sample, Loaded Statistics, Biased Induction, Biased Generalization)
A believes that statistics resulted from a poll taken in what is called “the bible belt” majority of which favored elimination of abortion is representing the attitude of all Americans (this is a biased polling).
Fallacy XIX: Burden of Proof
A claims that since B cannot prove that God does not exist, so he does (the opposit argument cannot be proven either).
Fallacy XX: Circumstantial Ad Hominem
A tells B that the reason she is against abortion is because she is a republican (political affiliation does not necessarily mean a political leaning towards any political ideology).
Fallacy XXI: Composition
A asserts that since a doctor aborted a fetus that was 7 months old, all the doctors aborting pregnancies are murderers (the action of one doctor cannot be generalized to all doctors).
Fallacy XXII: Confusing Cause and Effect (Questionable Cause)
Someone says sickness is as a result of depression. Since sick people are always in a depressed mood, therefore this statement has to be true (People who are sick are naturally depressed, the opposite cannot be true).
Fallacy XXIII: Division
A states that since a certain clinic is funded by a republican, all employees of the clinic are republicans as well (a part of something does not necessarily have all the characteristics of that thing).
Fallacy XXIV: False Dilemma (Black & White Thinking)
President Bush warned other nations after Sept. 11 that “you are either with the terrorists or against them” (one does not have to be for or against something).
Fallacy XXV: Gambler's Fallacy
Someone is watching a gambling table and notices that the dice has turned double six straight for two hours, he bets on double six because it is the right time for it (a common sequence of an event does not prove that the same thing will happen next).
Fallacy XXVI: Genetic Fallacy
A is certain that God exists since he was raised as a Christian (one should be able to change the belief he was brought up with).
Fallacy XXVII: Guilt By Association (Bad Company, Company that you keep)
A asks B what she thinks about God. B responds that if there is no physical evidence she cannot make any judgment. A says that the guy who killed the president said the same thing, therefore B belong to the same group of murderers (if one does something, someone with the same beliefs does not necessarily do the same thing).
Fallacy XXVIII: Hasty Generalization (Insufficient Sample, Leaping to A Conclusion, Hasty Induction)
A tells B that Iran has very hot climate because one summer he was to a central city in Iran and it was very hot (a certain season and a certain place does not determine the climate of the whole land at all times).
Fallacy XXIX: Ignoring a Common Cause (Questionable Cause)
A tells B that she is sneezing because of her usual allergy in allergy season. B says that she probably caught cold, but A insists that it is allergy (a common cause does not necessarily occur every time).
Fallacy XXX: Middle Ground (Golden Mean, Moderation)
In the movie “Fiddler of the Roof”, village men are gathered around the milk seller talking politics. One makes a comment against the Tsar. The milk seller approves his comments. Another speaks for the establishment. The milk seller approves points too. A third person objects to the milk seller how he could agree with both having two opposing points, at the same time. The milk seller tells the third person that he is completely right too (middle ground is not always an answer to two extremes).
Fallacy XXXI: Misleading Vividness
A tells B that he would never go back to Iran because of the violence he witnessed in the street. B tells him that he went during the uprising and that does not happen everyday. A says that he would never go back and adds: “you should have been there to see how they were beating up people!” (vividly expressing something does not prove the accurateness of the point).
Fallacy XXXII: Personal Attack (Ad Hominem Abusive)
A informs B that he would not go to a speech about cancer because the speaker talking about astronomy is against capital punishment (attacking one's personal belief in order to keep him quite or avoiding his voice being heard).
Fallacy XXXIII: Poisoning the Well
Don’t listen to him, he is nothing but a jerk (slandering someone and making that slander as a proof to attack the person).
Fallacy XXXIV: Post Hoc (Post Hoc Egro, Propter Hoc, False Cause)
A informs B of an earthquake of the next day. B asks what his evidence is. A says: “because last time it got hot like today, there was an earthquake the next day.” (The same condition will not necessarily happen after a similar situation).
Fallacy XXXV: Questionable Cause
A disregards the chain e-mail that says something bad would happen to him if he does not forward it. The next day he loses his job. He immediately forwards the e-mail to all his friends (a cause can be accidental).
Fallacy XXXVI: Red Herring (Smoke Screen, Wild Goose Chase)
A is explaining his absent of the day before to his friends. B asks A how his mother is doing after her sickness. A talks about his mother and his first story is forgotten (changing the subject by bringing up another subject unrelated to the first one).
Fallacy XXXVII: Relativist Fallacy (The Subjective Fallacy)
A tells B that he does not have to watch for cold virus because he never catches cold (insisting that one would not catch a disease although every one else has the potential of getting it).
Fallacy XXXVIII: Slippery Slope (The Camel’s Nose)
You cannot give one a break, or he would walk all over you (generalizing without evidence).
Fallacy XXXIX: Special Pleading
A asks B to cook for dinner. B says she is too tired after a full day work and A should cook. A says that he had a full day of work as well (pleading to something that does not solve the original issue).
Fallacy XXXX: Spotlight
A wishes to B that he was an actor. All TV programs he watch show the glamorous lives they have (there are always exceptions).
Fallacy XXXXI: Straw Man
A asserts that September 11 attack on world trade center proves that we need an increase in military budget in order to fight terrorism (creating an excuse to do ones plans).
Fallacy XXXXII: Two Wrongs Make a Right
A asserts that US attacking Afghanistan is justified because of the September 11 event (an eye for an eye would make all blind)!